Use the Laws of Logarithms to rewrite the expression below in a form with no logarithm of a product, quotient, or power. log, (x(x – 9)) O a. log 4 × - 9x O b. log 4 x + log 4 × – 9 O c. 2 log 4 x- log 4 9 O d. log 4 x- log 4 (x – 9) O e. log 4 x + log 4 (x – 9)

Q: Find the area of the region inside the circle r = 12 sin 0 and outside the cardioid r = 4+4 sin 0.…

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Q: Use an iterated integral to find the area of the region. dy dx = y 81 7 5 4 3 2 1- 1 2 3 4 6 8

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Q: V4-x² c 3-x²-y² x dz dy dx J_5+x²+y² A 128/15 B 16/89 23/6 D) 6

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Q: 3. dy Find if y 2xy - x: dx = cos X using implicit differentiat

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Q: Where is each function continuous? (a) f(x) = Vi %3D

A: According to the company rule we can answer only first question and rest can be reposted.

Q: Use Theorem 13.9 to find the directional derivative of the function at P in the direction to PQ

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Q: 13.3 PARTIAL DERIVATIVES 29-32 Evaluate the indicated partial derivatives. I 29. f(x, y) = 9 – x² –…

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Q: test the converg ence and divergence 27-1 2. (2h-1):

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Q: Write a definite integral that represents the area of the region. (Do not evaluate the integral.) dx…

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Q: In this question, the power series method is to be applied to find the general solution of a…

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Q: Solve the following differenti- d'y 3. +2y=e"; dx dx

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Q: 11 Evaluate the iterated integral. JJ, J, (x² + y² + z?) dx dy dz A 5 в) з D 10 00

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Q: Determine the volume of the solid obtained by roteting the region bounded by y=x^2-2 and y=x about…

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Q: Find the volume of the solid generated by revolving the region bounded by the graphs of the…

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Q: Directions: Evaluate the derivatives of the following functions with respect to x and simplify the…

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Q: The graph of y=- 50co has a horizontal shift of A units with respect to the graph of y= - 50cos(x).

A: This question is related to Trigonometric functions, we will solve it using given information.

Q: Use a triple integral to find the volume of the solid in the first octant bounded by the coordinate…

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Q: The critical values f(z) = "(1- z)°, for some positive constants a and b on 10, 1[ is/are a. b. tb…

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Q: Evaluate JJ xy dA, where R is the region in (1, 3) (5, 3) R (2, 1) (4, 1) A) 56 В) 67 с) 38 90

A: Explanation of the answer is as follows

Q: Determine the area of the region enclosed by y3x^2 and y=x^1/2

A: To find the area of the region enclosed by the given curves.

Q: Find the point of intersection (xo, Yo, zo) of the lines given as: y = 4 + 5t, z = 2 + t z = 3 + 21…

A: To find the point of intersection x0, y0, z0 of the lines given as: L1: x=7+t, y=4+5t, z=2+tL2:…

Q: Find the area of the region enclosed by the curves y = x² and y 4.x by integrating with respect to…

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Q: find the equation for x in y=3x-x^3

A: Solving

Q: Find the limit. NOTE: Enter the answer using round brackets. t2 + 8 1 lim t+o 5t2 + 6't (?,?) - (

A: We have to find limit of given function

Q: Using appropriate substitution xp: V9x2-36x + 37 Is equal to

A: We have to integrate given function

Q: Evaluate the integral by first reversing the order of integration. NOTE: Enter the exact answer. e…

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Q: Find the limit. NOTE: Enter the answer using round brackets. t2 + 6 1 lim t→+o \ 8t2+9' 6t (?, ?)

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Q: Evaluate the line integral using Green's Theorem and check the answer by evaluating it directly. O 4…

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Q: Question * Using the Nth term test for divergence 1 2n + 14 n=1 diverges since lim is equal to 1.…

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Q: bounded by the graphs of the equat y

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Q: True or False, and give a short reason: (a) If a function is differentiable, then it is continuous.…

A: Given problem:- True or False, and give a short reason:   (a) If a function is differentiable, then…

Q: Sketch the region enclosed by the curves and find its area. y = cos8x, y = 0, x = π/16, x = π/8

A: Given: y = cos8x, y = 0, x = π/16, x = π/8

Q: Find the volume of the solid that results when the shaded region is revolved about the indicated…

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Q: Find the length of the curve, L. y? = 64 (x + 5)* , 0 0

A: The solution is given in the next step.

Q: Verify Green's Theorem by evaluating both integrals v? dx + x2 dy dA ax for the given path. C:…

A: 9

Q: Question 2 Use spherical coordinates to find the volume of the solid. The solid enclosed by the…

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Q: Find the exact arc length of the curve over the stated interval. 1 1 Gy, from y =1 to y = 3 12 NOTE:…

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Q: (8) Using Taylor's formula, e" log(1 + is approximately equal to (a) x – xy (b) х — ху + 2 (c) x +…

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Q: SAQ 4.1 Taylor's Theorem Name: Year & Course: Date: Instructor: 1. Find a Maclaurin series expansion…

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Q: Find the volume of the solid that results when the shaded region is 8 revolved about the indicated…

A: Volume of revolution

Q: 4. Under the usual addition 47Z/2021Z .

A: A detailed solution is given below.

Q: 1. Sket dh the graph of the cylinder r = (y – 2)2 in R. %3D

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Q: Use Green's Theorem to evaluate the line integral. y² dx + xy C: boundary of the region lying…

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Q: Find the divergence of F(x, y, z) =(a -1 Y, y? + 1' 3xz2 + 2y ) at (2,0, – x COS

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Q: Find the following for the given equation. r(t) = (e, 5t?, 6 tan(t)) (a) r'(t) = (b) r"(t) = (c)…

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Q: <press the area of the given surface as an iterated double integral, and then find the surface area.…

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Q: Determine the surface area of the solid obtained by rotating y=v9-x from -2sxs2 about the x -axis.

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Q: 2. Determine whether the statement is True or False. If it is false, explain what makes it false, or…

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Q: Verify Green's Theorem by evaluating both integrals ам | y2 dx + x2 dy dA ду for the given path. C:…

A: Solution is given below:

Q: Use double integration to find the volume of the solid. ... 3 3x + 2y + 4z = 12 А) 6 B) 9 12 15

A: Let's find.